4,250 research outputs found
A Numerical Perspective on Hartree-Fock-Bogoliubov Theory
The method of choice for describing attractive quantum systems is
Hartree-Fock-Bogoliubov (HFB) theory. This is a nonlinear model which allows
for the description of pairing effects, the main explanation for the
superconductivity of certain materials at very low temperature. This paper is
the first study of Hartree-Fock-Bogoliubov theory from the point of view of
numerical analysis. We start by discussing its proper discretization and then
analyze the convergence of the simple fixed point (Roothaan) algorithm.
Following works by Canc\`es, Le Bris and Levitt for electrons in atoms and
molecules, we show that this algorithm either converges to a solution of the
equation, or oscillates between two states, none of them being a solution to
the HFB equations. We also adapt the Optimal Damping Algorithm of Canc\`es and
Le Bris to the HFB setting and we analyze it. The last part of the paper is
devoted to numerical experiments. We consider a purely gravitational system and
numerically discover that pairing always occurs. We then examine a simplified
model for nucleons, with an effective interaction similar to what is often used
in nuclear physics. In both cases we discuss the importance of using a damping
algorithm
Influence of cross-section geometry and wire orientation on the phonon shifts in ultra-scaled Si nanowires
Engineering of the cross-section shape and size of ultra-scaled Si nanowires
(SiNWs) provides an attractive way for tuning their structural properties. The
acoustic and optical phonon shifts of the free-standing circular, hexagonal,
square and triangular SiNWs are calculated using a Modified Valence Force Field
(MVFF) model. The acoustic phonon blue shift (acoustic hardening) and the
optical phonon red shift (optical softening) show a strong dependence on the
cross-section shape and size of the SiNWs. The triangular SiNWs have the least
structural symmetry as revealed by the splitting of the degenerate flexural
phonon modes and The show the minimum acoustic hardening and the maximum
optical hardening. The acoustic hardening, in all SiNWs, is attributed to the
decreasing difference in the vibrational energy distribution between the inner
and the surface atoms with decreasing cross-section size. The optical softening
is attributed to the reduced phonon group velocity and the localization of the
vibrational energy density on the inner atoms. While the acoustic phonon shift
shows a strong wire orientation dependence, the optical phonon softening is
independent of wire orientation.Comment: 10 figures, 4 Tables, submitted to JAP for revie
Computer simulations of ionic liquids at electrochemical interfaces
Ionic liquids are widely used as electrolytes in electrochemical devices. In
this context, many experimental and theoretical approaches have been recently
developed for characterizing their interface with electrodes. In this
perspective article, we review the most recent advances in the field of
computer simulations (mainly molecular dynamics). A methodology for simulating
electrodes at constant electrical potential is presented. Several types of
electrode geometries have been investigated by many groups in order to model
planar, corrugated and porous materials and we summarize the results obtained
in terms of the structure of the liquids. This structure governs the quantity
of charge which can be stored at the surface of the electrode for a given
applied potential, which is the relevant quantity for the highly topical use of
ionic liquids in supercapacitors (also known as electrochemical double-layer
capacitors). A key feature, which was also shown by atomic force microscopy and
surface force apparatus experiments, is the formation of a layered structure
for all ionic liquids at the surface of planar electrodes. This organization
cannot take place inside nanoporous electrodes, which results in a much better
performance for the latter in supercapacitors. The agreement between
simulations and electrochemical experiments remains qualitative only though,
and we outline future directions which should enhance the predictive power of
computer simulations. In the longer term, atomistic simulations will also be
applied to the case of electron transfer reactions at the interface, enabling
the application to a broader area of problems in electrochemistry, and the few
recent works in this field are also commented upon.Comment: 12 pages, 10 figures, perspective articl
Effect of dispersion interactions on the properties of LiF in condensed phases
Classical molecular dynamics simulations are performed on LiF in the
framework of the polarizable ion model. The overlap-repulsion and polarization
terms of the interaction potential are derived on a purely non empirical,
first-principles basis. For the dispersion, three cases are considered: a first
one in which the dispersion parameters are set to zero and two others in which
they are included, with different parameterizations. Various thermodynamic,
structural and dynamic properties are calculated for the solid and liquid
phases. The melting temperature is also obtained by direct coexistence
simulations of the liquid and solid phases. Dispersion interactions appear to
have an important effect on the density of both phases and on the melting
point, although the liquid properties are not affected when simulations are
performed in the NVT ensemble at the experimental density.Comment: 8 pages, 5 figure
Inverse design of cooperative electromagnetic interactions
The cooperative electromagnetic interactions between discrete resonators have
been widely used to modify the optical properties of metamaterials. Here we
propose a general evolutionary approach for engineering these interactions in
arbitrary networks of resonators. To illustrate the performances of this
approach, we designed by genetic algorithm, an almost perfect broadband
absorber in the visible range made with a simple binary array of metallic
nanoparticles
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